Browsing by Subject "Boundary value problems"
Now showing 1 - 8 of 8
Results Per Page
Sort Options
Item Open Access Analysis of a thin, penetrable, and nonuniformly loaded cylindrical reflector illuminated by a complex line source(Institution of Engineering and Technology, 2017) Oğuzer, T.; Kuyucuoglu, F.; Avgin, I.; Altıntaş, A.A thin, penetrable, and cylindrical reflector is illuminated by the incident field of a complex source point. The scattered field inside the reflector is not considered and its effect is modelled through a thin layer generalised boundary condition (GBC). The authors formulate the structure as an electromagnetic boundary value problem and two resultant coupled singular integral equation system of equations are solved by using regularisation techniques. The GBC provides us to simulate the thin layer better than the resistive model which is applicable only for very thin sheets. Hence, the more reliable data can be obtained for high-contrast and low-loss dielectric material. The scattering and absorption characteristics of the front-fed and offset reflectors are obtained depending on system parameters. Also, the effects of the edge loading are examined for both E- and Hpolarisations. The convergence and the accuracy of the formulation are verified in reasonable computational running time.Item Open Access Derivation of Closed-Form Green’s Functions for a General Microstrip Geometry(1992) Aksun, M.I.; Mittra, R.The derivation of the closed-form spatial domain Green’s functions for the vector and scalar potentials is presented for a microstrip geometry with a substrate and a super-state, whose thicknesses can be arbitrary. The spatial domain Green’s functions for printed circuits are typically expressed as Sommerfeld integrals, that are inverse Hankel transform of the corresponding spectral domain Green’s functions, and are quite time-consuming to evaluate. Closed-form representations of these Green’s functions in the spatial domains can only be obtained if the integrands are approximated by a linear combination of functions that are analytically integrable. In this paper, we show we can accomplish this by approximating the spectral domain Green’s functions in terms of complex exponentials by using the least square Prony’s method. © 1992 IEEEItem Open Access Dynamic boundary control of the timoshenko beam(Pergamon Press, 1992) Morgül, Ö.We consider a clamped-free Timoshenko beam. To stabilize the beam vibrations, we propose a dynamic boundary control law applied at the free end of the beam. We prove that with the proposed control law, the beam vibrations uniformly and exponentially decay to zero. The proof uses a Lyapunov functional based on the energy of the system. © 1992.Item Open Access A dynamic control law for the wave equation(Elsevier, 1994) Morgül, Ö.We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize the system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is restricted to be a positive real function which could be strictly proper. We then show that, if the transfer function of the controller is strictly proper, then the resulting closed-loop system is asymptotically stable, and if proper but not strictly proper, then the resulting closed-loop system is exponentially stable.Item Open Access Estimation of Spurious Radiation from Microstrip Etches Using Closed-Form Green’s Functions(IEEE, 1992) Aksun, M.I.; Mittra, R.The problem of spurious radiation from electronic packages is considered in this paper by investigating the power radiated from microstrip etches that are excited by arbitrarily-located current sources, and terminated by complex loads at both ends. The first step in the procedure is to compute the current distribution on the microstrip line by using the method of moments (MoM). Two novel contributions of this paper are: (i) employing the recently-derived closed-form Green’s functions in the spatial domain that permit an efficient computation of the elements of the MoM matrix; (ii) incorporating complex load terminations in a convenient manner with virtually no increase in the computation time. The computed current distribution is subsequently used to calculate the spurious radiated power and the result is compared with that derived by using an approximate, transmission line analysis. © 1992 IEEEItem Open Access On lifting of operators to Hilbert spaces induced by positive selfadjoint operators(Academic Press, 2005) Cojuhari, P.; Gheondea, A.We introduce the notion of induced Hilbert spaces for positive unbounded operators and show that the energy spaces associated to several classical boundary value problems for partial differential operators are relevant examples of this type. The main result is a generalization of the Krein-Reid lifting theorem to this unbounded case and we indicate how it provides estimates of the spectra of operators with respect to energy spaces. © 2004 Elsevier Inc. All rights reserved.Item Open Access On the stabilization and stability robustness against small delays of some damped wave equations(IEEE, 1995) Morgül, O.In this note we consider a system which can be modeled by two different one-dimensional damped wave equations in a bounded domain, both parameterized by a nonnegative damping constant. We assume that the system is fixed at one end and is controlled by a boundary controller at the other end. We consider two problems, namely the stabilization and the stability robustness of the closed-loop system against arbitrary small time delays in the feedback loop. We propose a class of dynamic boundary controllers and show that these controllers solve the stabilization problem when the damping coefficient is nonnegative and stability robustness problem when the damping coefficient is strictly positive.Item Open Access Validation of higher-order approximations and boundary conditions for lossy conducting bodies(Institute of Electrical and Electronics Engineers, 2014-09) Sukharevsky, Ilya O.; Altıntaş, AyhanThe problem of high-frequency diffraction by a smooth lossy body with high conductivity is considered. In addition to the geometrical optics approximation, additional asymptotic terms are derived to take into account the curvature of the boundary and material properties. Since these higher-order terms are derived by taking into account exact boundary conditions, it is easy to learn about the limitations of impedance conditions and to determine more accurate approximate conditions. The obtained higher-order boundary conditions and their limitations are numerically validated by solving Muller's second-kind integral equations. © 2014 IEEE.